一维非等温可压缩Navier-Stokes-Korteweg方程组稀疏波的整体稳定性（英文）

可压缩Navier-Stokes-Korteweg方程组可用来描述具有内部毛细作用的粘性可压缩流体的运动.本文研究了毛细系数依赖于密度、粘性系数和热传导系数依赖于温度的一维非等温的可压缩Navier-Stokes-Korteweg方程组Cauchy问题解的大时间行为.利用基本的L~2能量方法,我们证明如果相应的Euler方程组的黎曼问题存在稀疏波解,那么所考虑的一维可压缩Navier-Stokes-Korteweg方程组存在唯一的整体强解,并且当时间趋于无穷大时,此强解趋向于稀疏波.这里初始扰动和稀疏波的强度都可以任意大.     

一类带有非牛顿位势的可压缩Navier-Stokes方程整体强解的存在性

主要研究了一类带有非牛顿位势的可压缩Navier-Stokes方程:其中粘性系数μ依赖于密度ρ,Φ是非牛顿位势.证明了上述问题的强解的存在性.在相容性条件下,得到了强解的唯一性.     

粘性系数依赖于密度的Korteweg型不可压流体的强解问题

研究一类Korteweg型不可压流体模型的强解问题.针对粘性系数依赖于密度的情形,当初始值满足兼容性条件(9)对,证明了强解的局部存在性和唯一性.我们在这指出,本文允许初始真空存在.     

不可压缩向列型液晶系统Cauchy问题整体强解的存在性和大时间性质

本文研究非齐次不可压缩向列型液晶系统在三维全空间上的Cauchy问题.对任意的β∈(1/2,1],当初值的范数■充分小时,本文证明整体强解的存在性及大时间衰减估计,其中初始密度可含真空或具有紧支集.     

具有大初值和真空的Navier-Stokes-Maxwell方程组强解的全局存在性和唯一性

本文研究了一维空间中可压缩Navier-Stokes方程组,通过Lorentz力耦合Maxwell方程组的初边值问题,得到了在大初始值且带真空的情形下强解的全局存在性和唯一性.本文结果可视为带真空和大初值的强解全局存在性的第一个结果.     

多孔介质中两相不可压缩不易混溶渗流问题的特征配置法

多孔介质中两相不可压缩不易混溶渗流问题是非线性偏微分方程的耦合系统,其中压力方程是椭圆的用配置法逼近,而饱和度方程是对流占优的抛物方程,用特征配置法来逼近,并且证明了数值解的存在唯一性,最后得到了最优的误差估计.     

一类非自治发展方程一致吸引子的存在性

本文主要讨论一类非线性发展方程整体强解的长时间行为,利用文献[3]的方法,我们获得了整体强解对应的解过程族的一致耗散性,然后,通过验证一致(关于σ∈Σ)ω-极限紧,得到了系统的一致吸引子的存在性,其中非线性项满足临界指数增长条件.     

广义Tjon-Wu方程Cauchy问题强解的存在唯一性和稳态解的存在性

利用卷积的性质和schauder不动点原理等技巧,在L_(1,i)空间中证明了一类广义Tjon-Wu方程Cauchy问题强解的存在唯一性以及稳态解的存在性.     

具有奇性与真空粘性依赖于密度的非牛顿流局部强解的存在唯一性

研究一维有界区间上粘性依赖于密度且具有奇性、初始允许真空的可压缩非牛顿流.通过正则化奇性项以及逐步迭代构造初边值问题的逼近解,对逼近解取极限得到其局部强解的存在唯一性,进一步推广了相关文献中关于非牛顿流解的存在性结果.     

黏性依赖于密度的一维可压缩黏性辐射反应气体方程组的Cauchy问题

本文考虑一维可压缩黏性辐射反应气体方程组,对一类依赖于密度的、退化的黏性系数,得到了其Cauchy问题大初值非真空整体解的存在性.问题的关键在于如何得到密度和温度的正的上下界估计.     

Existence of solutions for the equations modeling the motion of rigid bodies in an ideal fluid

In this paper, we study the motion of rigid bodies in a perfect incompressible fluid. The rigid-fluid system fills a bounded domain in R³. Adapting the strategy from Bourguignon and Brezis (1974) [1], we use the stream lines of the fluid and we eliminate the pressure by solving a Neumann problem. In this way, the system is reduced to an ordinary differential equation on a closed infinite-dimensional manifold. Using this formulation, we prove the local in time existence and uniqueness of strong solutions.     

On the motion of rigid bodies in a viscous fluid

We consider the problem of motion of several rigid bodies in a viscous fluid. Both compressible and incompressible fluids are studied. In both cases, the existence of globally defined weak solutions is established regardless possible collisions of two or more rigid objects.     

On the motion of a rigid body immersed in a bidimensional incompressible perfect fluid

We consider the motion of a rigid body immersed in a bidimensional incompressible perfect fluid. The motion of the fluid is governed by the Euler equations and the conservation laws of linear and angular momentum rule the dynamics of the rigid body. We prove the existence and uniqueness of a global classical solution for this fluid–structure interaction problem. The proof relies mainly on weighted estimates for the vorticity associated with the strong solution of a fluid–structure interaction problem obtained by incorporating some viscosity.     

On Weak Solutions for Fluid‐Rigid Structure Interaction: Compressible and Incompressible Models

The purpose of this note is to derive compactness proporties for both incompressible and compressible viscous flows in a bounded domain interacting with a finite number of rigid bodies. We prove the global existence of weak solutions away from collisions AMS Subject Classification: 35Q10, 76D99, 73B99

Keywords: Fluid­structure interaction, rigid bodies, incompressible and compressible Navier­Strokes equations, weak solutions

     

On the Motion of Shear-Thinning Heat-Conducting Incompressible Fluid-Rigid System

The full Navier-Stokes-Fourier system with mixed boundary condition that describes the motion of shear-thinning and incompressible viscous fluid in a rotating multi-screw extruder is investigated. The viscosity is assumed to depend on the shear rate and the temperature. The global existence of suitable weak solutions is established. The fictitious domain method which consists in filling the moving rigid screws with the surrounding fluid and taking into account the boundary conditions on these bodies by introducing a well-chosen distribution of boundary forces is used.     

Existence of local strong solutions to fluid–beam and fluid–rod interaction systems

We study an unsteady nonlinear fluid–structure interaction problem. We consider a Newtonian incompressible two-dimensional flow described by the Navier–Stokes equations set in an unknown domain depending on the displacement of a structure, which itself satisfies a linear wave equation or a linear beam equation. The fluid and the structure systems are coupled via interface conditions prescribing the continuity of the velocities at the fluid–structure interface and the action-reaction principle. Considering three different structure models, we prove existence of a unique local-in-time strong solution, for which there is no gap between the regularity of the initial data and the regularity of the solution enabling to obtain a blow up alternative. In the case of a damped beam this is an alternative proof (and a generalization to non zero initial displacement) of the result that can be found in [20]. In the case of the wave equation or a beam equation with inertia of rotation, this is, to our knowledge the first result of existence of strong solutions for which no viscosity is added. The key points consist in studying the coupled system without decoupling the fluid from the structure and to use the fluid dissipation to control, in appropriate function spaces, the structure velocity.     

Unsteady flow of shear-thinning non-Newtonian incompressible fluid through a twin-screw extruder

The unsteady flow of viscous incompressible shear-thinning non-Newtonian fluid with mixed boundary is investigated. The boundary condition on the outflow is the modified natural boundary condition, it contains the additional nonlinear term, which enables us to control the kinetic energy of the backward flow. The global existence of weak solution is proved. The fictitious domain method which consists in filling the moving rigid screws with the surrounding fluid and taking into account the boundary conditions on these bodies by introducing a well-chosen distribution of boundary forces is used.     

Smooth solutions for the motion of a ball in an incompressible perfect fluid

In this paper we investigate the motion of a rigid ball surrounded by an incompressible perfect fluid occupying RN. We prove the existence, uniqueness, and persistence of the regularity for the solutions of this fluid-structure interaction problem.     

Global existence and zero α limit of the 3D incompressible two‐fluid MHD equations

In this paper, we establish global existence of strong solutions to the 3D incompressible two‐fluid MHD equations with small initial data. In addition, the explicit convergence rate of strong solutions from the two‐fluid MHD equations to the Hall‐MHD equations is obtained as . Copyright © 2017 John Wiley & Sons, Ltd.